On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

الملخص EN

A bounded linear operator T on a Hilbert space ℋ, satisfying ∥T2h∥2+∥h∥2≥2∥Th∥2 for every h∈ℋ, is called a convex operator.

In this paper, we give necessary and sufficient conditions under which a convex composition operator on a large class of weighted Hardy spaces is an isometry.

Also, we discuss convexity of multiplication operators.